Question

The diameter of yarn is ........... to the square roots of the cotton count.

• A. Equal
• B. Directly proportional
• C. Non-directly proportional
• D. Inversely proportional

Hint:

Always remember: Higher cotton count = finer yarn (smaller diameter). Formula: \( d \propto 1/\sqrt{N} \).

Answer 1

The Correct Option is D

Step 1: Understanding yarn count.
The cotton count system expresses the fineness of yarn.
It is defined as the number of hanks of 840 yards per pound of yarn.
A higher count means finer yarn, while a lower count means coarser yarn.
Step 2: Relation of count and diameter.
Yarn diameter is related to yarn count by the formula:
\[ \text{Diameter of yarn} \propto \frac{1}{\sqrt{\text{Count}}} \] This means the diameter is inversely proportional to the square root of the cotton count.
Step 3: Analysis of options.
- Equal: Incorrect, since they are not numerically equal.
- Directly proportional: Wrong, because higher count gives finer yarn, so diameter decreases.
- Non-directly proportional: Vague and not technically correct.
- Inversely proportional: Correct, since as count increases, diameter decreases proportionally to \(1/\sqrt{\text{Count}}\).
Step 4: Conclusion.
Thus, the diameter of yarn is inversely proportional to the square root of the cotton count.